Journal
PHYSICAL REVIEW LETTERS
Volume 121, Issue 16, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.121.167204
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Funding
- European Unions Horizon 2020 research and innovation program [ERC-StG-Neupert-757867-PARATOP]
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Artificial neural networks have been recently introduced as a general ansatz to represent many-body wave functions. In conjunction with variational Monte Carlo calculations, this ansatz has been applied to find Hamiltonian ground states and their energies. Here, we provide extensions of this method to study excited states, a central task in several many-body quantum calculations. First, we give a prescription that allows us to target eigenstates of a (nonlocal) symmetry of the Hamiltonian. Second, we give an algorithm to compute low-lying excited states without symmetries. We demonstrate our approach with both restricted Boltzmann machines and feed-forward neural networks. Results are shown for the one-dimensional spin1/2 Heisenberg model, and for the one-dimensional Bose-Hubbard model. When comparing to exact results, we obtain good agreement for a large range of excited-states energies. Interestingly, we find that deep networks typically outperform shallow architectures for high-energy states.
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